Simplify the expression. $(2z^{4}-5z^{3}+6z^{2})(4z^{3}-5z^{2})$
Answer: First use the distributive property. $ 2 z^4 (4 z^3) + 2 z^4 (-5 z^2) - 5 z^3 (4 z^3) - 5 z^3 (-5 z^2) + 6 z^2 (4 z^3) + 6 z^2 (-5 z^2) $ Simplify. $ 8z^{7} - 10z^{6} - 20z^{6} + 25z^{5} + 24z^{5} - 30z^{4} $ $8z^{7}-30z^{6}+49z^{5}-30z^{4}$ Identify like terms. $ { 8z^{7}} \color{#DF0030} {- 10z^{6}} \color{#DF0030} {- 20z^{6}} {+ 25z^{5}} {+ 24z^{5}} {- 30z^{4}} $ Add the coefficients. $ { 8z^{7}} \color{#DF0030} { -30z^{6}} {+ 49z^{5}} { -30z^{4}} $